Depending on how much luggage you have and how comfortable you are changing trains, could also consider walking from earl's court. It is only 10 minutes. If you go straight out of the station, cross the street, turn left then right onto Kenway. Kenway will take an abrupt left and there is a narrow pathway there that will take you to cross Cromwell on to Marloes rd. You go maybe a quarter mile, then right turn on Cheniston Gardens which will put you right in front of the Holiday Inn close. Look on google maps to confirm.

I have also heard (never tried it)that after dropping off the customs paperwork the bus driver can drop you off at the terminal and you could meet your wife at the tube Staton and ride together.

20 minute walk from the hotel to the natural history museum and science museum, both free. British museum (also free) is an easy bus or tube ride. All the other sites mentioned great as well. St.Paul's is 16 lbs, but beautiful and you can take stairs to a wrap around balcony near the top of the dome that gives an excellent panoramic view of the city, i much preferred over the London Eye. Google maps is your friend, tube is quick, but if it's a nice day riding the double decker buses can add to the sight seeing experience along the way.

I have brought my wife, mom, and daughter with me on layovers and had a great time every trip. Make sure they get business class on the way over and start checking the retuning loads early. Be prepared to send her back through a different city, Philly can work well.

Cheers